Little Help with a Calc Question

www.quickmath.com

the best site ever

 

damn, its been too long since calc two. Looks like integration by parts and substitution though.

 

Ok, i'll do the first one.

int(x^3)(e^-x^2)dx

let u=x^2

then

int[u*x*e^(-u)dx]
and dx = du*1/(2x)

so

int[u*x*e^(-u)(1/(2x)du) = 1/2*int[u*e^(-u)du]

by integration by parts:

1/2*int[u*e^(-u)du] = 1/2[-u*e^(-u) - int[1*e^(-u)du] = -1/2*u*e^(-u) + 1/2e^(-u) = -1/2*x^2*e^(-x^2) + 1/2e^(-x^2) = e^(-x^2)*(1-x^2)/2

 

For the second one, just substitute u=x+2. So you'll have (u-2)^3*u^(5/2). Expand the first term (u-2)^3 and you'll get something slight messy, but then you can multiply tern by term with u^(5/2), so you'll have a long polynomial with terms like u^(11/2). Then you can integrate those individually, like 12/13*u^(13/12).